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Hamilton-Connected Hourglass-free Line Graphs
- 来源：
- 学校官网
- 收录时间：
- 2026-04-05 14:13:43
- 时间：
- 2025-11-24 16:00:00
- 地点：
- 学活十层报告厅
- 报告人：
- Hong-Jian Lai
- 学校：
- 北京交通大学
- 关键词：
- Hamiltonian, line graphs, K_{1,3}-free, hourglass-free, P_n-free, Hamilton-connected, extremal graphs
- 简介：
- Motivated by Thomassen’s conjecture that every 4-connected line graph is Hamiltonian, and as line graphs are $K_{1,3}$-free graphs, many researchers have investigated the Hamiltonian properties of graphs forbidding certain induced graphs including $K_{1,3}$. The hourglass $\Gamma_0$ is the unique simple graph with degree sequence $(4,2,2,2,2)$ and $P_n$ is the path on $n$. In [Discrete Mathematics 341 (2018) 1806-1815], Z. Ryj\'{a}\v{c}ek, P. Vr\'{a}na and L. Xiong posed a conjecture that every 3-connected $\{K_{1,3}, \Gamma_0, P_{16}\}$-free graph is Hamilton-connected. X. Liu and L. Xiong proved this conjecture in [Discrete Mathematics 345(2022), 112910] proved this conjecture. We continue to study this problem aiming to characterize all extremal graphs. We have found a family ${\cal W}$ of graphs formed by subdividing the Wagner graph and by attaching pendent vertices, and prove that every 3-connected $\{K_{1,3}, \Gamma_0, P_{18}\}$-free graph $G$ is Hamilton-connected unless the Hamilton-connected closure of $G$ is a member of ${\cal W}$.
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报告介绍：
Motivated by Thomassen’s conjecture that every 4-connected line graph is Hamiltonian, and as line graphs are $K_{1,3}$-free graphs, many researchers have investigated the Hamiltonian properties of graphs forbidding certain induced graphs including $K_{1,3}$. The hourglass $\Gamma_0$ is the unique simple graph with degree sequence $(4,2,2,2,2)$ and $P_n$ is the path on $n$. In [Discrete Mathematics 341 (2018) 1806-1815], Z. Ryj\'{a}\v{c}ek, P. Vr\'{a}na and L. Xiong posed a conjecture that every 3-connected $\{K_{1,3}, \Gamma_0, P_{16}\}$-free graph is Hamilton-connected. X. Liu and L. Xiong proved this conjecture in [Discrete Mathematics 345(2022), 112910] proved this conjecture. We continue to study this problem aiming to characterize all extremal graphs. We have found a family ${\cal W}$ of graphs formed by subdividing the Wagner graph and by attaching pendent vertices, and prove that every 3-connected $\{K_{1,3}, \Gamma_0, P_{18}\}$-free graph $G$ is Hamilton-connected unless the Hamilton-connected closure of $G$ is a member of ${\cal W}$.
报告人介绍：
赖虹建教授是美国西弗吉尼亚大学数学系终身教授，博士生导师，国际知名的图论专家，主要研究领域包括图论中的欧拉子图、哈密尔顿性问题、整数流以及图论中的染色和连通度问题，在JCT(B),Combinatorica，SIAM J.DM.,JGT,Europ.J.Combin., EJC, DM等杂志发表学术论文250余篇，完成专著2部。曾任DM杂志客座编辑，现担任Applied Mathematics和Graphs and Combinatorics等多个杂志编委。
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